Brown believes the Dons will be his side's main challengers again this campaign, adding that the Reds have been exciting to watch in recent seasons.
"I think Aberdeen (will be our main rivals) after the last couple of seasons," Brown told Sky Sports News HQ.
"They have been exciting to watch, they've come to Celtic Park and got points and we have struggled up there so hopefully we can do a little bit better this season.
"Aberdeen have been great the past couple of seasons and so have Hearts as well coming up last year, so we expect more of the same from those two."
Source: Sky Sports